

Course 3, Unit 2  Inequalities and Linear Programming
Overview
This unit reviews and pulls together students' prior work with graphing
of linear, quadratic, and inverse variation functions; solving inequalities
graphically; solving quadratic equations algebraically; graphing linear
equations in two variables; and solving systems of linear equations in
two variables. Linearprogramming techniques are used to solve problems
in which the goal is to find optimum values of a linear objective function.
Key Ideas from Course 3, Unit 2

Write inequalities to express questions about functions of one
or two variables: In all the lessons of this unit, students
represent situations expressed in words in algebraic representations,
that is, inequalities and equalities of one and two variables.
An example of a onevariable inequality is a^{2} + 10a  7 ≤ 14.
An example of a twovariable inequality is 2x + y > 4.

Solve quadratic inequalities in one variable: Solution sets
are described symbolically, as a number line graph, and using interval
notation. (See pages 108117.)

Solving a linear inequality in two variables: Solutions sets
are represented graphically as halfplanes. (See pages 128131.)

Solving a system of two linear inequalities: Solution sets
are represented graphically as the region represented by both inequalities,
which is the intersection of the two halfplanes. (See pages 130131.)

Solve linear programming problems involving two independent variables: Linear
inequalities often represent constraints in a context such as the
productionscheduling problem on page 132. The feasible points
are the points that satisfy all of the constraints. The task in a
linearprogramming problem is to find a maximum or minimum (optimal)
solution for an objective function for the context. For the productionscheduling
problem that continues on page 137, the objective function is
the algebraic rule that shows how to calculate profit for the day. (See
pages 132142.)
